A right rectangular prism has an area of 29 square units and a height of 3 units. What is the volume
To find the volume of a rectangular prism, we multiply the area of the base by the height. Since the prism has a height of 3 units, we just need to find the area of the base and then multiply it by 3.
Given the area of 29 square units, we can write the equation:
base area × 3 = 29
Divide both sides of the equation by 3 to isolate the base area:
base area = 29 / 3
Since the prism is right rectangular, the base area is equal to the length times the width. Let's call the length L and the width W.
L × W = 29 / 3
We can find the possible combinations of L and W that satisfy this equation by listing out the factors of 29/3 (or 29/3, rounded to the nearest inch):
Factors of 29/3: 1, 29/3, 29/3, 29
Since the length and width must be positive integers and the area is greater than 1, the possible combinations are:
L = 1, W = 29/3, base area = L × W = 1 × 29/3 = 29/3
L = 29/3, W = 1, base area = L × W = 29/3 × 1 = 29/3
L = 29/3, W = 29/3, base area = L × W = 29/3 × 29/3 = 841/9
L = 29, W = 1/3, base area = L × W = 29 × 1/3 = 29/3
L = 1/3, W = 29, base area = L × W = 1/3 × 29 = 29/3
The base area can be 29/3 or 841/9, depending on our choice of length and width. However, since the area is given in square units, it is likely that the base area is 29/3, which represents an area of 29 square units. Therefore, the volume of the prism is:
Volume = base area × height = (29/3) × 3 = 87/3 = <<87/3=29>>29 units³
To find the volume of a right rectangular prism, we need to multiply the area of the base by the height.
Given that the area of the prism is 29 square units and the height is 3 units:
Volume = Area of the base x Height
Volume = 29 x 3
Volume = 87 cubic units
Therefore, the volume of the right rectangular prism is 87 cubic units.